Active Learning Lecture Slides For use with Classroom Response Systems Statistical Inference: Confidence Intervals

Copyright © 2013 Pearson Education, Inc. 8.1 A good point estimate has which of the following characteristics? a) Bias: None Standard Error: High b) Bias: High Standard Error: High c) Bias: None Standard Error: Low d) Bias: High Standard Error: Low

Copyright © 2013 Pearson Education, Inc. 8.1 A good point estimate has which of the following characteristics? a) Bias: None Standard Error: High b) Bias: High Standard Error: High c) Bias: None Standard Error: Low d) Bias: High Standard Error: Low

Copyright © 2013 Pearson Education, Inc. 8.2 When the sampling distribution is approximately normal, what is the margin of error equal to for a 95% confidence interval? a) 1.96 b) 1.96*standard error c) Standard error d) Point estimate 1.96*standard error

Copyright © 2013 Pearson Education, Inc. a) 1.96 b) 1.96*standard error c) Standard error d) Point estimate 1.96*standard error 8.2 When the sampling distribution is approximately normal, what is the margin of error equal to for a 95% confidence interval?

Copyright © 2013 Pearson Education, Inc. 8.3 In 2006 the GSS had a special topic that investigated disabilities. They asked respondents if they had difficulty fully participating in school, housework or other daily activities and 265 out of 2,749 said “yes”. What is the point estimate of the population proportion of Americans that have difficulty completing these tasks? a) 0.10 b) c) d) p e) Unknown

Copyright © 2013 Pearson Education, Inc. a) 0.10 b) c) d) p e) Unknown 8.3 In 2006 the GSS had a special topic that investigated disabilities. They asked respondents if they had difficulty fully participating in school, housework or other daily activities and 265 out of 2,749 said “yes”. What is the point estimate of the population proportion of Americans that have difficulty completing these tasks?

Copyright © 2013 Pearson Education, Inc. 8.4 True or False: A point estimate is better than an interval estimate because it gives you the exact value for which you are looking. a) True b) False

Copyright © 2013 Pearson Education, Inc. 8.4 True or False: A point estimate is better than an interval estimate because it gives you the exact value for which you are looking. a) True b) False

Copyright © 2013 Pearson Education, Inc. 8.5 True or False: An interval estimate gives you a region that the parameter has to fall within. a) True b) False

Copyright © 2013 Pearson Education, Inc. 8.5 True or False: An interval estimate gives you a region that the parameter has to fall within. a) True b) False

Copyright © 2013 Pearson Education, Inc. 8.6 The formula below gives a region of plausible values of : a) the population proportion b) the population mean c) the sample mean d) the sample proportion

Copyright © 2013 Pearson Education, Inc. 8.6 The formula below gives a region of plausible values of : a) the population proportion b) the population mean c) the sample mean d) the sample proportion

Copyright © 2013 Pearson Education, Inc. 8.7 In 2006 the GSS asked 2,986 people if they were very happy, pretty happy, or not too happy and 920 people said that they were very happy. Is the sample “large” enough to calculate the 95% confidence interval to estimate the proportion of all Americans that are very happy? a) Yes, there are more than 30 observations. b) Yes, there are more than 15 successes and 15 failures. c) No, there are not more than 15 successes and 15 failures. d) Cannot be determined.

Copyright © 2013 Pearson Education, Inc. 8.7 In 2006 the GSS asked 2,986 people if they were very happy, pretty happy, or not too happy and 920 people said that they were very happy. Is the sample “large” enough to calculate the 95% confidence interval to estimate the proportion of all Americans that are very happy? a) Yes, there are more than 30 observations. b) Yes, there are more than 15 successes and 15 failures. c) No, there are not more than 15 successes and 15 failures. d) Cannot be determined.

Copyright © 2013 Pearson Education, Inc. 8.8 In 2006 the GSS asked 2,986 people if they were very happy, pretty happy, or not too happy and 920 people said that they were very happy. Find the 95% confidence interval to estimate the proportion of all Americans that are very happy. a) (0, 0.02) b) (0.25, 0.37) c) (0.27, 0.35) d) (0.29, 0.32)

Copyright © 2013 Pearson Education, Inc. 8.8 In 2006 the GSS asked 2,986 people if they were very happy, pretty happy, or not too happy and 920 people said that they were very happy. Find the 95% confidence interval to estimate the proportion of all Americans that are very happy. a) (0, 0.02) b) (0.25, 0.37) c) (0.27, 0.35) d) (0.29, 0.32)

Copyright © 2013 Pearson Education, Inc Based off of the same sample, which of the confidence intervals for the population mean would be the widest? a) A 90% confidence interval b) A 95% confidence interval c) A 99% confidence interval d) Cannot be determined

Copyright © 2013 Pearson Education, Inc Based off of the same sample, which of the confidence intervals for the population mean would be the widest? a) A 90% confidence interval b) A 95% confidence interval c) A 99% confidence interval d) Cannot be determined

Copyright © 2013 Pearson Education, Inc The margin of error of a confidence interval of the population mean decreases as… a) the sample size decreases. b) the sample size increases. c) the sample mean increases. d) the sample mean decreases.

Copyright © 2013 Pearson Education, Inc The margin of error of a confidence interval of the population mean decreases as… a) the sample size decreases. b) the sample size increases. c) the sample mean increases. d) the sample mean decreases.

Copyright © 2013 Pearson Education, Inc The General Social Survey included a question about how many hours the respondent spent doing religious activities outside of their own home. For the 1,414 respondents the sample mean was 6.15 hours and the sample standard deviation was hours. Find the 95% confidence interval for the population mean amount of time spent doing religious activities outside of their own home. a) (5.43, 6.87) b) (-26.24, 38.55) c) (5.29, 7.01) d) (5.03, 7.27)

Copyright © 2013 Pearson Education, Inc The General Social Survey included a question about how many hours the respondent spent doing religious activities outside of their own home. For the 1,414 respondents the sample mean was 6.15 hours and the sample standard deviation was hours. Find the 95% confidence interval for the population mean amount of time spent doing religious activities outside of their own home. a) (5.43, 6.87) b) (-26.24, 38.55) c) (5.29, 7.01) d) (5.03, 7.27)

Copyright © 2013 Pearson Education, Inc The General Social Survey included a question about how many hours the respondent spent doing religious activities outside of their own home. For the 1,414 respondents the sample mean was 6.15 hours and the sample standard deviation was hours. What can we say about the distribution of hours spent doing religious activities? a) It is bell shaped. b) It is right skewed. c) It is left skewed. d) Nothing can be determined.

Copyright © 2013 Pearson Education, Inc The General Social Survey included a question about how many hours the respondent spent doing religious activities outside of their own home. For the 1,414 respondents the sample mean was 6.15 hours and the sample standard deviation was hours. What can we say about the distribution of hours spent doing religious activities? a) It is bell shaped. b) It is right skewed. c) It is left skewed. d) Nothing can be determined.

Copyright © 2013 Pearson Education, Inc Which of the following is NOT a property of the t distribution? a) It is symmetric. b) It is indexed by a degree of freedom equal to n - 1. c)It has more spread in the tails than the normal distribution. d)The shape becomes closer and closer to the normal distribution as n decreases.

Copyright © 2013 Pearson Education, Inc Which of the following is NOT a property of the t distribution? a) It is symmetric. b) It is indexed by a degree of freedom equal to n - 1. c)It has more spread in the tails than the normal distribution. d)The shape becomes closer and closer to the normal distribution as n decreases.

Copyright © 2013 Pearson Education, Inc A marketing researcher is interested in estimating the mean amount of money spent on lunch by college students. The average amount spent on lunch by a random sample of 10 students is $6.30 with a standard deviation of $2.21. Find the 95% confidence interval for the population mean amount spent on lunch every day. a) b) c)

Copyright © 2013 Pearson Education, Inc A marketing researcher is interested in estimating the mean amount of money spent on lunch by college students. The average amount spent on lunch by a random sample of 10 students is $6.30 with a standard deviation of $2.21. Find the 95% confidence interval for the population mean amount spent on lunch every day. a) b) c)

Copyright © 2013 Pearson Education, Inc In 2002 a local survey (using a SRS) found that 13.4% of people strongly agreed with the statement that “More parking meters should be installed downtown.” Using the 2002 data as a guideline, determine the sample size needed to estimate the proportion of people that would agree for the current year within 0.01 at 95% confidence. a) 4458 b) 3140 c) 45 d) 23

Copyright © 2013 Pearson Education, Inc In 2002 a local survey (using a SRS) found that 13.4% of people strongly agreed with the statement that “More parking meters should be installed downtown.” Using the 2002 data as a guideline, determine the sample size needed to estimate the proportion of people that would agree for the current year within 0.01 at 95% confidence. a) 4458 b) 3140 c) 45 d) 23

Copyright © 2013 Pearson Education, Inc Suppose that you were interested in determining the proportion of Americans that agreed with the statement that “Taxes should not be raised for any reason.” Assuming that you have no idea what proportion will agree with this statement, determine the sample size needed to estimate the proportion of people that agree for the current year within 0.01 at 95% confidence. a) 16,513 b) 9,604 c) 4,458 d) 4,900 e) 49

Copyright © 2013 Pearson Education, Inc Suppose that you were interested in determining the proportion of Americans that agreed with the statement that “Taxes should not be raised for any reason.” Assuming that you have no idea what proportion will agree with this statement, determine the sample size needed to estimate the proportion of people that agree for the current year within 0.01 at 95% confidence. a) 16,513 b) 9,604 c) 4,458 d) 4,900 e) 49

Copyright © 2013 Pearson Education, Inc Suppose that you are interested in estimating the population mean entry salary of engineers. You think that entry salaries probably range from $30,000 to $100,000 and the distribution of salaries is bell shaped. You want to be accurate to within $3,000 of the population mean entry salary and be 95% confident. What size sample do you need? a) 100 b) 87 c) 59 d) 8 e) Cannot be determined

Copyright © 2013 Pearson Education, Inc Suppose that you are interested in estimating the population mean entry salary of engineers. You think that entry salaries probably range from $30,000 to $100,000 and the distribution of salaries is bell shaped. You want to be accurate to within $3,000 of the population mean entry salary and be 95% confident. What size sample do you need? a) 100 b) 87 c) 59 d) 8 e) Cannot be determined

Copyright © 2013 Pearson Education, Inc Suppose that you want to estimate the entry level salaries of high school teachers for the state of Nebraska. A previous study had $1700 listed as the sample standard deviation. You want to have a 90% confidence interval with a margin of error of $250. How large a sample do you need? a) 178 b) 126 c) 91 d) 12 e) Cannot be determined

Copyright © 2013 Pearson Education, Inc Suppose that you want to estimate the entry level salaries of high school teachers for the state of Nebraska. A previous study had $1700 listed as the sample standard deviation. You want to have a 90% confidence interval with a margin of error of $250. How large a sample do you need? a) 178 b) 126 c) 91 d) 12 e) Cannot be determined

Copyright © 2013 Pearson Education, Inc Suppose that you are a writer for a university newspaper and due to time constraints you conduct a survey of only 20 randomly selected students. You ask them, “Do you plan to watch the homecoming parade?” and 19 of them say they plan to watch. Create a 95% confidence interval for the proportion of students that plan on watching the parade. a) (0.85, 1) b) (.74, 1) c) (.76,.99) d) Cannot be determined

Copyright © 2013 Pearson Education, Inc Suppose that you are a writer for a university newspaper and due to time constraints you conduct a survey of only 20 randomly selected students. You ask them, “Do you plan to watch the homecoming parade?” and 19 of them say they plan to watch. Create a 95% confidence interval for the proportion of students that plan on watching the parade. a) (0.85, 1) b) (.74, 1) c) (.76,.99) d) Cannot be determined

Copyright © 2013 Pearson Education, Inc The margin of error of a confidence interval estimates the error… a) caused by bad sampling techniques. b) caused by measurement error. c) caused by not controlling lurking variables. d) caused by using a sample rather than the whole population. e) all of the above.

Copyright © 2013 Pearson Education, Inc The margin of error of a confidence interval estimates the error… a) caused by bad sampling techniques. b) caused by measurement error. c) caused by not controlling lurking variables. d) caused by using a sample rather than the whole population. e) all of the above.

Copyright © 2013 Pearson Education, Inc The bootstrap method is a method that constructs a confidence interval by… a) repeatedly sampling from the population. b) repeatedly sampling from the sample. c) repeatedly sampling from the sampling distribution. d) none of the above.

Copyright © 2013 Pearson Education, Inc The bootstrap method is a method that constructs a confidence interval by… a) repeatedly sampling from the population. b) repeatedly sampling from the sample. c) repeatedly sampling from the sampling distribution. d) none of the above.

Copyright © 2013 Pearson Education, Inc Why is the bootstrap method used? a) Because it is easier than traditional methods. b) Because it can be used when the formula for the confidence interval cannot easily be found mathematically. c) Because it uses additional sampling – this makes the confidence interval much better than traditional methods. d) Because it allows us to use 10,000 samples rather than just 1 sample that is used in traditional methods.

Copyright © 2013 Pearson Education, Inc Why is the bootstrap method used? a) Because it is easier than traditional methods. b) Because it can be used when the formula for the confidence interval cannot easily be found mathematically. c) Because it uses additional sampling – this makes the confidence interval much better than traditional methods. d) Because it allows us to use 10,000 samples rather than just 1 sample that is used in traditional methods.

Copyright © 2013 Pearson Education, Inc To make a 90% confidence interval for the population median using the bootstrap method you first randomly select 20,000 separate samples of size 8 from the original data and then you compute the medians from each of the new samples. What is the next step? a) Find the average and standard deviation of the 20,000 medians. Then, compute a traditional 95% confidence interval ( ) with those values. b) Find the 2.5 th and 97.5 th percentile of the medians, this is your confidence interval. c) Find the 5 th and 95 th percentiles of the medians, this is your confidence interval.

Copyright © 2013 Pearson Education, Inc. a) Find the average and standard deviation of the 20,000 medians. Then, compute a traditional 95% confidence interval ( ) with those values. b) Find the 2.5 th and 97.5 th percentile of the medians, this is your confidence interval. c) Find the 5 th and 95 th percentiles of the medians, this is your confidence interval To make a 90% confidence interval for the population median using the bootstrap method you first randomly select 20,000 separate samples of size 8 from the original data and then you compute the medians from each of the new samples. What is the next step?